The problem of determining properties of an unknown function by evaluating it at scattered points arises in many different contexts. If the function is arbitrary, it may be necessary to evaluate the function at all points in its domain; however, when the function is well-behaved, it is often possible to determine global information with relatively few probes (evaluations). The determination of zero of a monotonic function is a classic example of this problem; other examples include finding the extremum of a unimodal function, the game of Battleship, and geometric probing in which one wants to find various shape parameters of an object by probing it at the fewest possible points. This research applies an approach, based on Kraft's inequality, to such discrete search problems. Using generalization of Kraft's inequality to prove lower bounds are applicable to problems in which an algorithm for the problem can be mapped to a computation tree; Kraft's inequality then captures the minimum ``degree of imbalance'' that must be present in any computation tree solving the problem.
